Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.
Permutations - dCode
Tag(s) : Combinatorics
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Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.
Item permutations consist in the list of all possible arrangements and ordering of elements in any order.
Example: The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A
Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).
The best-known method is the Heap algorithm (method used by this dCode's calculator).
Step 1 - for each item, fix it at the beginning
Step 2 - repeat step 1 with the remaining items
Permutations can thus be represented as a tree of permutations:
Counting permutations uses combinatorics and factorials
Example: For $ n $ items, the number of permutations is equal to $ n! $ (factorial of $ n $)
Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.
Example: DCODE 5 letters have $ 5! = 120 $ permutations but contain the letter D twice (these $ 2 $ letters D have $ 2! $ permutations), so divide the total number of permutations $ 5! $ by $ 2! $: $ 5!/2!=60 $ distinct permutations.
Permutations makes exponential values which needs huge computing servers with huge memory cells, so the generation must be paid.
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